Recent content by yankees26an

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    Proof by Induction: Solving Homework Involving Prods & Sums

    \prod_{j=1}^{k+1}_{j} - 1 = \prod_{j=1}^{k+1}_{j} - 1 + (k+1) \prod_{j=1}^{k+1}_{j} Ok so I also cancel out the -1 on both sides, then I factor out \prod_{j=1}^{k+1}_{j} and I get \prod_{j=1}^{k+1}_{j} = 1 +(k+1)(\prod_{j=1}^{k+1}_{j}) then cancel out the...
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    Proof by Induction: Solving Homework Involving Prods & Sums

    Ok so first I replaced all the sum stuff with the right hand side to make it easier to read. By substituting the right side of left side of the initial equality with the right side. That should work fine right? The I have: \prod_{j=1}^{k+1}_{j} - 1 = \prod_{j=1}^{k+1}_{j} - 1 +...
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    Proof by Induction: Solving Homework Involving Prods & Sums

    Can you give an example?
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    Proof by Induction: Solving Homework Involving Prods & Sums

    Yes. This requires that I need to add some term to both sides. Not really sure what term I need to use to construct the induction for k+1
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    Proof by Induction: Solving Homework Involving Prods & Sums

    Homework Statement \sum_{i=1}^{n} (i \prod_{j=1}^{i}_{j}) = \prod_{i=1}^{n+1}_{i} - 1 Homework Equations The Attempt at a Solution First show the base case. That easys just shows it holds for n=1. Not sure where to go from there? What term do I add to both sides? Not really sure what...
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    Proving by Induction: Sum of i(i+1)(i+2)

    Ok so I simplified and it's 1/4 (n+1) (n+2) (n+3) (n+4) So what do I do after I simplify?
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    Proving by Induction: Sum of i(i+1)(i+2)

    You completely lost me.. What's on the left side and the right side?
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    Proving by Induction: Sum of i(i+1)(i+2)

    Did you take the (n+1)(n+2)(n+3) from the right side or from the i's? What happens to the extra (n+1)(n+2)(n+3) terms on the right?
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    Proving by Induction: Sum of i(i+1)(i+2)

    Ok, so basically just plugin n+1 for i on the left, and simplify the right. Set them equal, and done?
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    Proving by Induction: Sum of i(i+1)(i+2)

    Homework Statement Prove by induction, that for all integer n where n>= 1 \sum_{i=1}^{n} i(i+1)(i+2) = \frac{n(n+1)(n+2)(n+3)}{4} Homework Equations The Attempt at a Solution First question is do I start at i=0 or i=1? It says >=, so not sure. Ok then I added...
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    Proving by Induction: P(n) for n>1

    Can you explain what you did? Ok I'm still a bit confused To show its true for n=2 I do 1/1^2+ 1/2^2 <(2 - 1/1) + (2- 1/2) Is that how you prove it for n=2?
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    Proving by Induction: P(n) for n>1

    I don't follow. Can you explain a bit or give an example?
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    Proving by Induction: P(n) for n>1

    Homework Statement Prove by induction that for an integer n where n>1 , http://img3.imageshack.us/img3/5642/prob1q.jpg Homework Equations The Attempt at a Solution Prove P(2) is true then prove P(x) = P(x+1) is true, then it's true for all x That's all I really from proof...
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    Solving Isobaric Process Heat Addition Problem

    Yea I realized that and used the other equation after some trial and error. Cp for a monoatomic gas is 5/2R :) Solved.
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    Differences in Water Pressure in a Horizontal Pipe with Changing Radius

    Any hints? choice 1: pressure? If so, how?